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The History of the Universe
Hot Cool
High density Low density
Planck time
Inflation
Nucleosynthesisof H, He, Li
Decoupling of CMB
Galaxy Formation
Now
Astronomy in 1936
• ~1770: Messier catalogue • 1888: NGC, IC catalogues • Van Maanen’s “contribution”• 1920: Curtis-Shapley debate• 1923: Hubble measured distance
to M31 • 1929: Expanding universe• 1936: Realm of the Nebulae
described Hubble classification system.
100 inch telescopeCompleted 1918
Edwin Hubble
The Types of
Galaxies
Ellipticals Barred Spirals
Spirals
Also…Irregulars
Usual classes used at current time:• E0-E7• S0, Sa, Sab, Sb, Sbc, Sc, Scd, Sd, Sdm, Sm, Im, Ir (or amorphous)• SB0, SBa, SBab, SBb, SBbc, SBc, SBcd, SBd, SBdm, SBm
General Properties of Galaxy Types• E
• MB = -8 to less than –23• Mass = 107 – 1013 M• diameters <1 kpc – hundreds of kpc
• S• MB = -16 to –23 • Mass = 109 – 1012 M• luminous diameters 5-100 kpc
• Irr• MB = -13 to –20 • Mass = 108 – 1010 M• luminous diameters 1–10 kpc
E0 E710*(1-b/a)
b
a
Sa Sc• Bulge:disk ratio• Tightness of winding• Resolution of arms into star
clusters & H II regions.
Spirals
EllipticalsBarred Spirals Irregulars
Morphological Types of Local Galaxies
(images taken from Frei, Guhathakurta, Gunn & Tyson
1996)
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Homework Assignment No. 1Due Jan 16 (Friday)
Classifying Galaxies
Good news, Professor Hubble! Even though it is 1936, you have been awarded access to the internet (at only $39.95/month, directly chargeable to your VISA card). So you don’t have to waste any more time freezing at telescopes in order to classify galaxies. You can just look at them over the web! Here’s how:
• Find a computer with decent bandwidth over the internet.• Point your web browser to www. stsci.edu• Click on “Digitized sky survey” on the side-bar.• Now click on “retrieve image data” buried in the middle of the text.• Set “File Format” to GIF. (You may have to reset this each time you get a new image).• Leave the other defaults alone: “First Generation Survey”, etc.• Look at the images of the galaxies at the coordinates listed below.• Write down your best guess at the Hubble class of each galaxy, with a brief description
of the galaxy and of why you gave it whatever Hubble class you picked.
RA Dec Epoch12 20 07 29 16 50 J200012 48 36 -05 48 00 J2000
Distribution of galaxy types
• Dense regions (cluster centers) predominantly ellipticals.
• Field galaxies predominantly spirals.
• On average, roghly even split between E and S.
E
S
S0
Log (Projected surface density of galaxies)
Frac
tion
of p
opul
atio
n
Total number of galaxies
Dressler 1980
Spiral galaxies
• Holmberg radius rH
• Length of semi-major axis down to 26.5 B-mag arcsec –2
• Effective radius re
• Radius within which ½ of light is emitted.
• Disks follow exponential law
• Freeman’s law• Most disks have about same surface brightness at their centers• Reason not clear• This observational result is now in dispute
USE TRANSPARENCY
Rotation Curves• Spherical mass shell, uniform density:
• Fcentripital = Fgravity
• Inside spherical mass distribution:
• Outside mass distribution:
• Sph. Distr. + exponential disk
USE TRANSPARENCY
Show spectrograph slit positions
Mass Determinations for Spiral Galaxies
Rotation Curves
• Flat rotation curves dark matter
M33 Rotation curve
Density Distribution of Dark Matter halo
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Mass determinations fromabsorption line widths
• Virial Theorem 2K = -U<v2> = 3 <vr
2> σ2
r = GM/(5R)• See pp. 1005-1008, + Sect. 2.4
• Applied to nuclei of spirals presence of massive black holes
• Also applied to• E galaxies• Galaxy clusters
The Virial Theorem [CO 2.4]
• For gravitationally bound systems in equilibrium• Total energy = ½ time-averaged potential energy.
E = total energyU = potential energy.K = kinetic energy.
E = K + U
• Can show from Newton’s 3 laws + law of gravity:• ½ (d2I/dt2 ) -2K = U where I = Σmiri
2 = moment of inertia.
• Time average < d2I/dt2 > = 0, or at least ~ 0.
• Virial theorem -2<K> = <U> <K> = - ½ <U>
<E> = <K> + <U> <E> = ½ <U>
Mass to Light Ratios: Evidence for Dark Matter Tuning-Fork Diagram
Trends in spiral galaxies(see CO Tables 23.1/23.2)
• Mass/Light ratios• Sa Sc : M/LB = 6.2 2.6• Sc’s dominated by younger, hotter, more
massive stars.• Colors
• Sa Sc : B-V = 0.75 0.52• Bluer colors Sc’s dominated by younger,
hotter stars.• Mgas/Mtotal
• Sa Sd: Mgas/Mtotal = 0.04 0.25• Molecular/atomic hydrogen
• Sa Sd: MH2/MHI = 2.2 0.3• Metallicity
• Depends on absolute magnitude• No. of Globular Clusters/Total Luminosity
CO Fig 23.12
dE,∆ E
SIrr
E, dE
S, Irr
CO Fig 23.10
Tully-Fisher Relation
• Maxiumum rotation velocity-Luminosity relation [FIG 23.8]
• Tully-Fisher relation [FIG 23.9]• MB = -9.95 log10VMax + 3.15 (Sa)• MB = -10.2 log10VMax + 2.71 (Sb)• MB = -11.0 log10VMax + 3.31 (Sc)
• Follows from M(r)= v2r/G
Rotation Curves
CO Semi-Derivation
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Spiral Structure[CO 23.3]
Grand design (10%) Multi-arm (60%) Flocculent (30%)M51 M101 NGC 2841
Inner rings Outer RingNGC 7096 M81 NGC 4340
What causes spiral structure?
• Winding up of arms• Due to differential rotation
• Stochastic, Self-Propagating Star Formation• Chain-reaction star formation• SN shells shock fronts density enhancements
star formation more SN• Differential rotation then winds these regions up into
spiral patterns
• Density Waves • Wave in gravitational potential• Orbital velocity of stars different than pattern speed
• Stars, gas bunch up at position of spiral arms• Causes higher grav. Potential
• Unclear if self-sustaining or forced.
Spiral Arms & the Interstate Highway
• Density wave• Spiral arms have higher density than space between arms• Excess gravitational attraction slows down gas, stars when they pass through
spiral arm in course of their orbits.• spiral arms are a traffic jam
Epicycles… the short form.For lurid details, see [CO pp.1018-1030]
Define an effective potential:
Taylor series expansion around position of minimum Φeff (circular orbit):
Circular symmetry independent of φ
Separate d2r/dt2 into R, φ, z components3 equations.
Conservation of specific angular
momentumJZ = R2 d φ/dt
Conservation of JZacceleration in
φ direction when rchanges.
PtolemyAlexandria, 140AD
(23.25-23.26)
(23.11)
(23.13-23.15)
Harmonic oscillation in R, φ, z about circular orbit(Epicycles)
Ωlp calculated from rotation curve for Milky Way.
Rm = R at min. ΦeffΩ = circular ang. vel.
Orbits closed if: m (Ω - Ωlp) = nκ
In inertial frame:
Viewed from frame rotating with Ωlp:
Two ways to line up closed elliptical orbits(as seen from frame rotating with Ωlp)
Basic nature of a density waveFrom: Toomre, Annual Review of Astronomy & Astrophysics, 1977 Vol. 15, 437.
• At each Rm , stars’ positions in epicycles are forced into a specific pattern by gravitational potential of spiral arm.
• Sum of positions of stars at this Rm forms an ellipse rotating at pattern speed.
• Spiral density pattern is sum of many ellipses, all rotating at same pattern speed.
Pendulum example
5
Lin & Shu’s theory
Fluid hydrodynamics
Perturbed form of collisionless Boltzmann equation.“quite complicated”
Inner Lindblad Resonance (ILR)Co-rotation RadiusOuter Lindblad Resonance (OLR)
Density wave theory interprets most spirals as 2-armed• 4-armed pattern is n / m = 1 / 4• exists over a narrow range of radius.
less likely to be seen.
•Actual 4-armed spirals are superposition of two 2-armed patterns
Important in all disk galaxies
Density waves cannot propagate across ILR or OLR
Spiral Structure[CO 23.3]
Grand design (10%) Multi-arm (60%) Flocculent (30%)M51 M101 NGC 2841
Inner rings Outer RingNGC 7096 M81 NGC 4340
M81 spiral structure at different wavelengths
UV: hot stars Near IR: late-type starsVisible: stars + obscuration
21 cm: HI
Old red population shows small but
real spiral density enhancement.
Passage of gas through spiral arms
Calculated streamlines for gas
Response of gas to density waves
• Simple pendulum model• Each pendulum = 1 gas cloud• For large amplitude forcing,
pendulums collide.• shock fronts in spiral arms
• HI map (right) shows velocity jumps at spiral arms.
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Orbits in Barred Spirals
• Gas avoids “co-rotation” radius in barred potential.• Causes “Fig-8” shape in rotation curve.
Kinematics of gas, in [NII][BM] Fig 4.60
ROUND BULGE PEANUT-SHAPED
Stable orbits (stars) Max. gas density
Gas velocityGas density
Trailing vs. leading spiralsWhich is the near side of the galaxy?
Molecular clouds on inner edges of arms
CO contours over red image
CO contours over 21 cm map
Swing Amplification
Automatically converts any leading spirals into much stronger trailing spirals.
Position of (leading) spiral density enhancement
Epicyclic orbit of star
Spiral Structureof the Milky Way
• New model• Lepine et al (2001)
ApJ 546, 234.• mix of
• 2-armed mode• 4-armed mode
• Sun at ~ co-rotation radius.
From HI (21 cm observations)assuming circular rotation.
N-body simulation
Hard to measure, because we are
inside it.
Map of nearby young objects
Summary: Density Waves?• Evidence showing density waves do occur.
• Old, red stars show spiral density perturbation.• Molecular clouds form on inner edges of spiral arms.• HI gas flow shows discontinuity due to shocks at inner edges of spiral
arms.• Bright young stars also in narrow arms.
• Observed width ∆θ ~ t*(Ω - Ωp) , as predicted.• Are these waves self-sustaining over 1010 years? Problems:
• Lin-Shu theory is linear; does not predict whether waves will grow or decay.
• How are density waves initially formed?• The usual interpretation
• Density waves need a driving force• Satellite galaxy at co-rotation radius (M51)• Bars
• Otherwise, act to prolong life of transitory phenomena.• Other mechanisms probably also important.
• Swing-amplification efficiently builds up temporary trailing spirals.
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